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<p><b>Index of Supplementary Materials</b></p>

<p>Title of paper: <i>A fractional inpainting model based on the vector-valued Cahn--Hilliard equation</i></p>

<p>Authors: <i>Jessica Bosch, Martin Stoll</i></p>


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<p>File: <a href="TwoStripes_orig.eps">TwoStripes_orig.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: original black-and-white stripe image in high quality </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="TwoStripes_damage.eps">TwoStripes_damage.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: damaged black-and-white stripe image in high quality </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="TwoStripes_Matlab.eps">TwoStripes_Matlab.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality black-and-white stripe image after using the MATLAB function inpaintn </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="TwoStripes_BPFA.eps">TwoStripes_BPFA.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality black-and-white stripe image after using the BPFA </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="TwoStripes_heat.eps">TwoStripes_heat.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality black-and-white stripe image after heat equation inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="TwoStripes_TV.eps">TwoStripes_TV.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality black-and-white stripe image after TV inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="TwoStripes_TV4.eps">TwoStripes_TV4.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality black-and-white stripe image after TV-Hminus1 inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="TwoStripes_CH.eps">TwoStripes_CH.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality black-and-white stripe image after standard vector-valued Cahn--Hilliard inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="TwoStripes_CH1p6.eps">TwoStripes_CH1p6.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality black-and-white stripe image after fractional (fractional power: 1.6) vector-valued Cahn--Hilliard inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="TwoStripes_CHbit.eps">TwoStripes_CHbit.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality black-and-white stripe image after bitwise binary Cahn--Hilliard inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="SixStripes_orig.eps">SixStripes_orig.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: original gray value stripe image in high quality  </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="SixStripes_damage.eps">SixStripes_damage.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: damaged gray value stripe image in high quality  </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="SixStripes_Matlab.eps">SixStripes_Matlab.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality gray value stripe image after using the MATLAB function inpaintn </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="SixStripes_BPFA.eps">SixStripes_BPFA.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality gray value stripe image after using the BPFA </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="SixStripes_heat.eps">SixStripes_heat.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality gray value stripe image after heat equation inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="SixStripes_TV.eps">SixStripes_TV.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality gray value stripe image after TV inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="SixStripes_TV4.eps">SixStripes_TV4.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality gray value stripe image after TV-Hminus1 inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="SixStripes_CH.eps">SixStripes_CH.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality gray value stripe image after standard vector-valued Cahn--Hilliard inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="SixStripes_CH1p6.eps">SixStripes_CH1p6.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality gray value stripe image after fractional (fractional power: 1.6) vector-valued Cahn--Hilliard inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="SixStripes_CHbit.eps">SixStripes_CHbit.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality gray value stripe image after bitwise binary Cahn--Hilliard inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="SixStripes_2p0.eps">SixStripes_2p0.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality gray value stripe image after vector-valued Cahn--Hilliard inpainting with fractional power 2.0 </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="SixStripes_1p9.eps">SixStripes_1p9.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality gray value stripe image after vector-valued Cahn--Hilliard inpainting with fractional power 1.9 </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="SixStripes_1p7.eps">SixStripes_1p7.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality gray value stripe image after vector-valued Cahn--Hilliard inpainting with fractional power 1.7 </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="SixStripes_1p5.eps">SixStripes_1p5.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality gray value stripe image after vector-valued Cahn--Hilliard inpainting with fractional power 1.5 </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="SixStripes_1p3.eps">SixStripes_1p3.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality gray value stripe image after vector-valued Cahn--Hilliard inpainting with fractional power 1.3 </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="SixStripes_1p1.eps">SixStripes_1p1.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality gray value stripe image after vector-valued Cahn--Hilliard inpainting with fractional power 1.1 </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="Fingerprint_orig.eps">Fingerprint_orig.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: original fingerprint image in high quality </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="Fingerprint_cluster.eps">Fingerprint_cluster.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: clustered fingerprint image after k-means clustering with 10 gray values </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="Fingerprint_origDamage.eps">Fingerprint_origDamage.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: damaged fingerprint image in high quality </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="Fingerprint_Matlab.eps">Fingerprint_Matlab.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality fingerprint image after using the MATLAB function inpaintn </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="Fingerprint_BPFA.eps">Fingerprint_BPFA.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality fingerprint image after using the BPFA </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="Fingerprint_heat.eps">Fingerprint_heat.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality fingerprint image after heat equation inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="Fingerprint_TV.eps">Fingerprint_TV.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality fingerprint image after TV inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="Fingerprint_TV4.eps">Fingerprint_TV4.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality fingerprint image after TV-Hminus1 inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="Fingerprint_CH.eps">Fingerprint_CH.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality fingerprint image after standard vector-valued Cahn--Hilliard inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="Fingerprint_CH1p8.eps">Fingerprint_CH1p8.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality fingerprint image after fractional (fractional power: 1.8) vector-valued Cahn--Hilliard inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="Fingerprint_CHbit.eps">Fingerprint_CHbit.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality fingerprint image after bitwise binary Cahn--Hilliard inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="Hill_orig.eps">Hill_orig.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: original hill image in high quality </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="Hill_cluster.eps">Hill_cluster.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: clustered fingerprint image after k-means clustering with 15 gray values </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="Hill_origDamage.eps">Hill_origDamage.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: damaged hill image in high quality </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="Hill_Matlab.eps">Hill_Matlab.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality hill image after using the MATLAB function inpaintn </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="Hill_BPFA.eps">Hill_BPFA.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality hill image after using the BPFA </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="Hill_heat.eps">Hill_heat.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality hill image after heat equation inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="Hill_TV.eps">Hill_TV.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality hill image after TV inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="Hill_TV4.eps">Hill_TV4.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality hill image after TV-Hminus1 inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="Hill_CH.eps">Hill_CH.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality hill image after standard vector-valued Cahn--Hilliard inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="Hill_CH1p8.eps">Hill_CH1p8.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality hill image after fractional (fractional power: 1.8) vector-valued Cahn--Hilliard inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="Hill_CHbit.eps">Hill_CHbit.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality hill image after bitwise binary Cahn--Hilliard inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="mSL_phantom.eps">mSL_phantom.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: original phantom image (with 5 metal regions) in high quality </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="mSL_sinogram.eps">mSL_sinogram.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: (damaged) sinogram of the original phantom image in high quality </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="FBP.eps">FBP.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: Filtered back projection (FBP) from the (damaged) sinogram. </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="CTsino_CH.eps">CTsino_CH.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality sinogram image after standard vector-valued Cahn--Hilliard inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="CTsino_CH1p8.eps">CTsino_CH1p8.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality sinogram image after fractional (fractional power: 1.8) vector-valued Cahn--Hilliard inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="CTsino_CH1p6.eps">CTsino_CH1p6.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality sinogram image after fractional (fractional power: 1.6) vector-valued Cahn--Hilliard inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="CTphantom_CH.eps">CTphantom_CH.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality phantom image after standard vector-valued Cahn--Hilliard inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="CTphantom_CH1p8.eps">CTphantom_CH1p8.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality phantom image after fractional (fractional power: 1.8) vector-valued Cahn--Hilliard inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="CTphantom_CH1p6.eps">CTphantom_CH1p6.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality phantom image after fractional (fractional power: 1.6) vector-valued Cahn--Hilliard inpainting </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="CT_10slices_3D.eps">CT_10slices_3D.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: 3D visualization of MRI slices in high quality </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="MRI_slice1.eps">MRI_slice1.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: original lower slice (slice 1.0) of the MATLAB MRI data set </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="MRI_slice2.eps">MRI_slice2.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: original upper slice (slice 2.0) of the MATLAB MRI data set </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="CH_slice1p2-1100.eps">CH_slice1p2-1100.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality virtual slice (slice 1.2) image after vector-valued Cahn--Hilliard inpainting with fractional power 1.8 </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="CH_slice1p4-1100.eps">CH_slice1p4-1100.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality virtual slice (slice 1.4) image after vector-valued Cahn--Hilliard inpainting with fractional power 1.8 </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="CH_slice1p6-1100.eps">CH_slice1p6-1100.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality virtual slice (slice 1.6) image after vector-valued Cahn--Hilliard inpainting with fractional power 1.8 </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="CH_slice1p8-1100.eps">CH_slice1p8-1100.eps</a></p>  <!-- same name twice -->

<p>Type: PostScript figure </p>

<p>Contents: high quality virtual slice (slice 1.8) image after vector-valued Cahn--Hilliard inpainting with fractional power 1.8 </p>

<p>Justification: improving visual comparisons  </p>



<p>File: <a href="inpaint_vectorFracCH_2D.m">inpaint_vectorFracCH_2D.m</a></p>  <!-- same name twice -->

<p>Type: MATLAB code </p>

<p>Contents: implementation of a fractional inpainting model based on the vector-valued Cahn--Hilliard equation in two spatial dimensions </p>

<p>Justification: comparisons and reproducing the results  </p>



<p>File: <a href="inpaint_vectorFracCH_3D.m">inpaint_vectorFracCH_3D.m</a></p>  <!-- same name twice -->

<p>Type: MATLAB code </p>

<p>Contents: implementation of a fractional inpainting model based on the vector-valued Cahn--Hilliard equation in three spatial dimensions </p>

<p>Justification: comparisons and reproducing the results  </p>



<p>File: <a href="dctn.m">dctn.m</a></p>  <!-- same name twice -->

<p>Type: MATLAB code </p>

<p>Contents: N-D discrete cosine transform </p>

<p>Justification: used in our implementation  </p>



<p>File: <a href="idctn.m">idctn.m</a></p>  <!-- same name twice -->

<p>Type: MATLAB code </p>

<p>Contents: N-D inverse discrete cosine transform </p>

<p>Justification: used in our implementation  </p>



<p>File: <a href="ssim.m">ssim.m</a></p>  <!-- same name twice -->

<p>Type: MATLAB code </p>

<p>Contents: implementation for calculating the structural similarity (SSIM) index between two images </p>

<p>Justification: used in our implementation  </p>



<p>File: <a href="Stripes.mat">Stripes.mat</a></p>  <!-- same name twice -->

<p>Type: MAT-file </p>

<p>Contents: data set for the gray value stripe image example in the paper </p>

<p>Justification: comparisons and reproducing the results  </p>



<p>File: <a href="MRI_data.mat">MRI_data.mat</a></p>  <!-- same name twice -->

<p>Type: MAT-file </p>

<p>Contents: data set for the MRI images example in the paper </p>

<p>Justification: comparisons and reproducing the results  </p>

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